@inproceedings{FalcaoCruzMalonek,
  author    = {Falc{\~a}o, M. Irene and Cruz, J. F. and Malonek, Helmuth Robert},
  title     = {REMARKS ON THE GENERATION OF MONOGENIC FUNCTIONS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2939},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29390},
  pages     = {18},
  abstract  = { In this paper we consider three different methods for generating monogenic functions. The first one is related to Fueter's well known approach to the generation of monogenic quaternion-valued functions by means of holomorphic functions, the second one is based on the solution of hypercomplex differential equations and finally the third one is a direct series approach, based on the use of special homogeneous polynomials. We illustrate the theory by generating three different exponential functions and discuss some of their properties. Formula que se usa em preprints e artigos da nossa UI\&D (acho demasiado completo): Partially supported by the R\\&D unit \emph{Matem\'atica a Aplica\c\~es} (UIMA) of the University of Aveiro, through the Portuguese Foundation for Science and Technology (FCT), co-financed by the European Community fund FEDER.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{MalonekFalcaoSilva,
  author    = {Malonek, Helmuth Robert and Falc{\~a}o, M. Irene and Silva, Ant{\´o}nio},
  title     = {MAPLE TOOLS FOR MODIFIED QUATERNIONIC ANALYSIS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2953},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29535},
  pages     = {7},
  abstract  = {At the 16th IKM Bock, Falc{\~a}o and G{\"u}rlebeck presented examples of the application of some specially developed Maple-Software in hypercomplex analysis. Other papers of those authors continued this work and showed the efficiency of such tools for concrete numerical calculations as well as for numerical experiments, supporting the detection of new relationships and even theorems in a highly technical theoretical work. The mentioned software has been developed mainly for the use on mapping problems in the Euclidean spaces of dimension 3 and 4 by means of Bergman kernel methods (BKM), which are related to monogenic functions as solutions of generalized Cauchy-Riemann equations with respect to the Euclidean metric (Riesz system). The developed procedures concerning generalized powers of totally regular variables and the corresponding homogeneous polynomials basically rely on results and conventions introduced in the paper "Power series representation for monogenic functions in Rm+1 based on a permutational product", Complex Variables, 15, No.3, 181-191 (1990) by H. Malonek. Since 1992 H. Leutwiler, S. L. Eriksson and others developed in a number of papers a modified Clifford analysis and, particularly, a modified quaternionic analysis. The modification mainly consists in considering generalized Cauchy-Riemann equations with respect to a hyperbolic metric in a half space. The aim of this contribution is to show how through a change of the basic combinatorial relations used in the modified quaternionic analysis the aforementioned Maple-software (that has been recently published on CD-Rom as integrated part of the text book "Funktionentheorie in der Ebene und im Raum" by K. G{\"u}rlebeck, K. Habetha, and W. Spr{\"o}ssig, in the series "Grundstudium Mathematik" of Birkh{\"a}user Verlag, 2006) can directly be used for numerical calculations in the modified theory.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}